The range of the wavelengths of audible sound in air is from about 0.0172 m to 17.2 m
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Further explanation
Let's recall the speed of wave and intensity of wave formula as follows:
[tex]\large {\boxed {v = \lambda f}}[/tex]
f = frequency of wave ( Hz )
v = speed of wave ( m/s )
λ = wavelength ( m )
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[tex]\large {\boxed {I = 2 \pi^2 A^2 f^2 \rho v}}[/tex]
I = intensity of wave ( W/m² )
A = amplitude of wave ( m )
f = frequeny of wave ( Hz )
ρ = density of medium ( kg/m³ )
v = speed of wave ( m/s )
Let's tackle the problem!
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Given:
minimum frequency = f_min = 20.0 Hz
maximum frequency = f_max = 2.00 × 10⁴ Hz
speed of sound in air = 343 m/s ( assumption )
Asked:
minimum wavelength = λ_min = ?
maximum wavelength = λ_max = ?
Solution:
[tex]20.0 \leq f \leq 2.00 \times 10^4[/tex]
[tex]20.0 \leq \frac{v}{\lambda} \leq 2.00 \times 10^4[/tex]
[tex]20.0 \leq \frac{343}{\lambda} \leq 2.00 \times 10^4[/tex]
[tex]\frac{343}{2.00 \times 10^4} \leq \lambda \leq \frac{343}{20.0}[/tex]
[tex]\large {\boxed {0.01715 \texttt{ m} \leq \lambda \leq 17.15 \texttt{ m}}}[/tex]
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Learn more
- Doppler Effect : https://brainly.com/question/3841958
- Example of Doppler Effect : https://brainly.com/question/810552
- Sound Waves Cannot Travel In Space. : https://brainly.com/question/546436
- Frequency of The Beats - Doppler Effect : https://brainly.com/question/12367463
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Answer details
Grade: College
Subject: Physics
Chapter: Sound Waves
